2006-2007, Term 2 (Winter)
MA3F4 - Linear Analysis
***ANSWERING SESSION*** on Thursday 31 May,
2-4pm and 5-6pm, in B2.06.
Here is the official
site from the department.
Time & Place: Tue
12-1 in MS.04, Fri 2-4 in MS.05.
Support classes: Tue
10-11 in MA_B3.01, by Michael
Doré.
Assessment:
3-hour examination.
Description:
Linear Analysis extends
Linear Algebra to infinite dimensional vector spaces. Functions form
linear spaces of infinite dimension, and differentiation is a linear
operation. Among the numerous applications of linear analysis is the
study of ODE's and PDE's.
We will introduce Banach and Hilbert spaces, and linear maps
(operators) between them. Four major theorems will be discussed:
Hahn-Banach, uniform boundedness (Banach-Steinhaus), open mapping, and
closed graph. These theorems have interesting consequences, in
particular regarding the spectrum of linear operators.
Syllabus:
- Banach spaces
- Baire Category Theorem and its consequences
- Hilbert spaces
- Bounded operators in Hilbert spaces
- Unbounded operators
Assignments:
References:
- Linear Functional
Analysis, by B. P. Rynne
and M. A. Youngston, Springer
(2001)
- Linear Analysis,
by B. Bollobas, Cambridge
Univ. Press (1990)
- Introductory
Functional Analysis with Applications, by E. Kreyszig, Wiley (1978)
- Functional Analysis,
by K. Yosida, Springer (1980)
- Applied Analysis,
by J. K. Hunter and B. Nachtergaele (2001)
- Real Analysis,
by G. B. Folland, Wiley (1999)
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